Pregunta
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Question 2
In a normal distribution, what is the appreximate
percentage of scores with a -score less than
A.
B
C.
D.

Ask by Elliott Chang. in Australia
Mar 30,2025

Solución de inteligencia artificial de Upstudy

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Approximately of scores have a -score less than .

Solución

  1. The standard normal distribution is symmetric about , meaning that of the scores lie below the mean.
  2. The empirical rule (or the rule) tells us that approximately of scores fall within standard deviation of the mean, i.e., between and .
  3. Since of the scores fall below and an additional fall between and , approximately
    of scores are below .
  4. Therefore, the approximate percentage of scores with a -score less than is .
Thus, the correct answer is © .

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Beyond the Answer

In a normal distribution, a -score of indicates that the score is 1.7 standard deviations above the mean. Using the empirical rule and standard normal distribution tables, we find that approximately 95% of scores fall within 2 standard deviations (both above and below the mean). Therefore, the percentage of scores with a -score less than is typically around , which points toward option D, being the most closely correct choice.
Now for a little fun, if you picture the normal distribution curve like a giant bell made of marshmallow fluff, each -score is like a point on that bell, telling you how far away from the delicious middle (the mean) you are! The further you go, the less “fluff” (or chance) you have—kind of like how the further you get from a party, the fewer cookies you might snag. So remember, most people (or scores) cluster around the mean, making it the life of the mathematical party!

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